Strong Hyperbolicity of Second-Order PDEs via Matrix Pencils
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910021915246592 |
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| author | Abalos, Fernando Hilditch, David |
| author_facet | Abalos, Fernando Hilditch, David |
| contents | We introduce a definition of strong hyperbolicity for second order partial differential equations using second order pencils. We show that this definition is equivalent to the standard one, derived by reducing the equations to first order form, but with the benefit of simplifying the calculations necessary to check hyperbolicity. In addition, we observe an interesting property, namely that when a system is strongly hyperbolic, its second order pencil can be factorized as a product of two diagonalizable first order pencils. Finally, we present an application to a vector potential for of Maxwell's equations, with a general extension and gauge fixing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13223 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong Hyperbolicity of Second-Order PDEs via Matrix Pencils Abalos, Fernando Hilditch, David Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics 83C05, 35L15, 35Q75, 35Q61, 15A22 We introduce a definition of strong hyperbolicity for second order partial differential equations using second order pencils. We show that this definition is equivalent to the standard one, derived by reducing the equations to first order form, but with the benefit of simplifying the calculations necessary to check hyperbolicity. In addition, we observe an interesting property, namely that when a system is strongly hyperbolic, its second order pencil can be factorized as a product of two diagonalizable first order pencils. Finally, we present an application to a vector potential for of Maxwell's equations, with a general extension and gauge fixing. |
| title | Strong Hyperbolicity of Second-Order PDEs via Matrix Pencils |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics 83C05, 35L15, 35Q75, 35Q61, 15A22 |
| url | https://arxiv.org/abs/2602.13223 |